Stochastic Hill Climbing with Learning by Vectors of Normal Distributions Second Corrected and Enhanced Version

This paper describes a stochastic hill climbing algorithm named SHCLVND to optimize arbitrary vectorial < n ! < functions. It needs less parameters. It uses normal (Gaussian) distributions to represent probabilities which are used for generating more and more better argument vectors. The-parameters of the normal distributions are changed by a kind of Hebbian learning. Kvasnicka et al. KPP95] used algorithm Stochastic Hill Climbing with Learning (HCwL) to optimize a highly multimodal vectorial function on real numbers. We have tested proposed algorithm by optimizations of the same and a similar function and show the results in comparison to HCwL. In opposite to it algorithm SHCLVND desribed here works directly on vectors of numbers instead their bit-vector representations and uses normal distributions instead of numbers to represent probabilities. 1 Overview In Section 2 we give an introduction with the way to the algorithm. Then we describe it exactly in Section 3. There is also given a compact notation in pseudo PASCAL-code, see Section 3.4. After that we give an example: we optimize highly multimodal functions with the proposed algorithm and give some visualisations of the progress in Section 4. In Section 5 there are a short summary and some ideas for future works. At last in Section 6 we give some hints for practical use of the algorithm. 2 Introduction This paper describes a hill climbing algorithm to optimize vectorial functions on real numbers. 2.1 Motivation Flexible algorithms for optimizing any vectorial function are interesting if there is no or only a very diicult mathematical solution known, e.g. parameter adjustments to optimize with respect to some relevant property the recalling behavior of a (trained) neuronal net HKP91, Roj93], or the resulting image of some image-processing lter.